2D Asymmetric Tensor Analysis

Abstract:

Analysis of degenerate tensors
is a fundamental step in finding the topological
structures and separatrices in tensor fields.
Previous work in this area have been
limited to analyzing symmetric second order tensor fields.
In this paper,
we extend the topological analysis to
2D general (asymmetric) second order tensor fields.
We show that it is not sufficient to
define degeneracies based on eigenvalues alone,
but one must also include the eigenvectors in the analysis.
We also study the behavior of these eigenvectors
as they cross from one topological region into another.